SOLUTION: suppose that the end points of the longer leg of a 30-60-90 triangle are (-3,5) and (2-1). what is the length of the shorter leg?

Algebra ->  Triangles -> SOLUTION: suppose that the end points of the longer leg of a 30-60-90 triangle are (-3,5) and (2-1). what is the length of the shorter leg?      Log On


   

Question 703753: suppose that the end points of the longer leg of a 30-60-90 triangle are (-3,5) and (2-1). what is the length of the shorter leg?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The difference in x-coordinates between point (-3,5) and point(2,-1) is
2-%28-3%29=2%2B3=5.
The difference in y-coordinates between point (-3,5) and point(2,-1) is
5-%28-1%29=5%2B1=6.
The length of the longer leg connection those two points is
longer leg = sqrt%285%5E2%2B6%5E2%29=sqrt%2825%2B36%29=sqrt%2861%29
That is not a friendly number.

Had the second point been (1,-2), the length would have been much friendlier:


In a 30-60-90 triangle the shorter leg is opposite the smaller, 30%5Eo angle, and the longer leg is adjacent to the 30%5Eo angle, so
tan%2830%5Eo%29=sqrt%283%29%2F3=(shorter leg)/(longer leg) --> shorter leg =%28sqrt%283%29%2F3%29(longer leg)

So, if longer leg = sqrt%2861%29
Shorter leg = %28sqrt%283%29%2F3%29sqrt%2861%29=sqrt%283%2A61%29%2F3=sqrt%28183%29%2F3= about 4.5
The drawing below shows one of the four possible such triangles (with the vertices circled):
All 4 have the red leg and a short leg on a perpendicular green line, but they could be flipped.